Inference of house-time varying signals on graphs emerges naturally during a plethora of network science related applications. A frequently encountered challenge pertains to reconstructing such dynamic processes, given their values over a subset of vertices and time instants. This Project develops a graph-aware kernel-primarily based kriged Kalman filter that accounts for the spatio-temporal variations, and offers economical on-line reconstruction, even for dynamically evolving network topologies. The kernel-primarily based learning framework bypasses the need for statistical data by capitalizing on the smoothness that graph signals exhibit with respect to the underlying graph. To handle the challenge of choosing the appropriate kernel, the proposed filter is combined with a multikernel choice module. Such a data-driven method selects a kernel attuned to the signal dynamics on-the-fly among the linear span of a preselected dictionary. The novel multikernel learning algorithm exploits the eigenstructure of Laplacian kernel matrices to scale back computational complexity. Numerical tests with synthetic and real knowledge demonstrate the superior reconstruction performance of the novel approach relative to state-of-the-art alternatives.

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